Torn Rotator Cuff?

I had a complete tear of my super spinatus and a torn labrum from a dislocation. I got the rotator cuff repaired in a mini-open procedure and that took about three months to heal. It took another three months to be back to full strength. Then, two years later (last year) I got the labrum fixed arthroscopically. That only took six weeks to heal. I never really lost strength from that because of PT going into and out of the procedure. Both times they were in my shoulder they reshaped the bones to open the space and remove spurs.
My worked on shoulder (dominant side) is now much better than the other side.
A 50% tear sounds like it will heal if you don't make it worse. I went for many years with a completely torn cuff. I just learned to do things differently, like not making a throwing motion. The pain was extreme when I did something wrong. I'm very happy with my operations.
You should consider if it will be easier or harder to get an operation in the future, otherwise just try the PT.

[Blueface]

I have had a slight tear on each of my rotator cuffs. Fortunately, not at the same time.
Both tears confirmed via MRI.
Saw dr's for surgery both times.
Both dr's told me the same thing, may or may not improve.

Instead of surgery, I did the same with the second tear since it worked so well for the first.
I did physical therapy and lots of it at home, on my own, with a towel while in the shower.
I used the towel and my good arm to aid the hurting one stretch gradually every day.

I ended up being fine. I still have an occasional flare up but the major pain is long gone.
No surgery done and glad I went this route.

In your case, 50% tear sounds way more than what I had.